Package 'scmix'

Rubin's rules pooling

Description

Pools estimates and variances across completed data sets from scmix_impute.

Usage

rubin_pool_scmix(completed, est_fun, var_fun)

Arguments

completed	list of completed data matrices.
est_fun, var_fun	functions mapping a completed matrix to a named numeric vector of estimates and matching variances.

Value

List with pooled estimates, total variance, standard errors, degrees of freedom, and 95 percent interval endpoints.

Examples

Y <- scmix_sim_mw3(n = 120, seed = 7)$Y
set.seed(7)
Y[sample(length(Y), 30)] <- NA
imp <- scmix_impute(Y, M = 2, K = 4, n_iter = 300, burn = 100, seed = 8)
pool <- rubin_pool_scmix(imp$completed, colMeans,
                         function(d) apply(d, 2, stats::var) / nrow(d))
pool$est
pool$se

---

Bayesian sparse conditional mixture clustering

Description

Fits the Bayesian sparse conditional mixture model of Dong, Liao, and Lee to a numeric data matrix and returns a clustering. Each mixture component factorizes into a chain of univariate polynomial regressions (degree m) with per-component, per-equation Bayesian variable selection under a centered Zellner g-prior; the number of clusters is selected within the run by an overfitted sparse mixture (Dirichlet concentration a = 1/K). A single run returns the estimated number of clusters, a label-invariant consensus partition, selection probabilities for every term of every within-component regression, and coefficient summaries.

Usage

scmix(
  Y,
  K = 7L,
  m = 2L,
  n_iter = 1500L,
  burn = 600L,
  order = NULL,
  a = 1/K,
  g = NULL,
  enum_max = 12L,
  seed = NULL,
  verbose = 0L,
  ...
)

Arguments

Y	numeric matrix (n x p); rows are observations. Must be complete for m >= 2.
K	integer, overfitted cap on the number of components (the number of occupied components is estimated; K only needs to exceed the plausible truth). Default 7.
m	integer polynomial degree of the conditional means (2 = quadratic, the recommended default; 1 = linear).
n_iter, burn	total and burn-in Gibbs sweeps.
order	optional integer permutation of 1:p giving the conditioning order. Defaults to the column order of Y. For m >= 2, results depend on the order (see the paper's order-sensitivity study); an inflated number of clusters relative to other orders is a practical misfit diagnostic.
a	Dirichlet concentration of the mixture weights (default 1/K; must be small for superfluous components to empty out).
g	g-prior scale: NULL (default) uses unit information g = n_k per component; a number fixes g; a function(nk) is evaluated per component. See the paper for the effect on the sigma^2 posterior at extreme signal-to-noise ratios.
enum_max	exact enumeration of selection sets while a regression has at most enum_max candidate terms; larger sets use validated single-flip Metropolis-Hastings. Default 12; 6 is a good speed/exactness compromise in higher dimension.
seed	optional integer seed (full run reproducibility).
verbose	print progress every verbose sweeps (0 = silent).
...	further arguments passed to the engine (see scmix_engine), e.g. n_min, nflip.

Value

An object of class "scmix": a list with components

cluster

integer vector, the consensus partition (Dahl's least-squares criterion over the posterior similarity matrix).

K

number of clusters in the consensus partition.

Kstar_mode

posterior mode of the number of occupied components across sweeps.

inclusion

list (one matrix per mixture component label) of posterior selection probabilities; rows = equations, columns = candidate terms (named).

beta, sig2

coefficient summaries (posterior means conditional on inclusion) and residual-variance posterior means, per label.

alive_frac

fraction of post-burn-in sweeps each label was occupied (interpret per-label summaries only for labels with alive_frac near 1).

z_draw

the final-sweep posterior draw of the allocations (a sample, not a point estimate; prefer cluster).

order, call, runtime

bookkeeping.

References

Dong, A., Liao, Y.-L., and Lee, D. (2026). Replacing three nested searches with one sweep: a Bayesian treatment of sparse conditional mixture clustering. Melnykov, V. and Wang, Y. (2023). Conditional mixture modeling and model-based clustering. Pattern Recognition 133, 108994. doi:10.1016/j.patcog.2022.108994 Dahl, D. B. (2006). Model-based clustering for expression data via a Dirichlet process mixture model. In Bayesian Inference for Gene Expression and Proteomics, 201–218. Cambridge University Press.

Examples

set.seed(1)
n <- 200
x1 <- rnorm(n)
x2 <- c(0.5 + x1[1:100]^2, -2 - 0.8 * x1[101:200]^2) + rnorm(n, 0, 0.6)
fit <- scmix(cbind(x1, x2), K = 5, m = 2, n_iter = 400, burn = 150,
             seed = 42)
fit$K            # curved clusters found from one run
table(fit$cluster, rep(1:2, each = 100))
summary(fit)

---

Adjusted Rand index

Description

The adjusted Rand index between two partitions (Hubert and Arabie, 1985); label-invariant, 1 for identical partitions, ~0 for unrelated ones.

Usage

scmix_ari(a, b)

Arguments

a, b	Two label vectors of equal length.

Value

The adjusted Rand index, a scalar.

Examples

a <- rep(1:3, each = 5)
b <- c(rep(2:1, each = 5), rep(3, 5))   # same partition, labels permuted
scmix_ari(a, b)

---

Low-level engine (advanced use)

Description

The validated sampling engine underlying scmix and scmix_impute, exposed for power users; see the package source for complete documentation of every argument and output.

Usage

scmix_engine(Y, ...)

Arguments

Y	numeric matrix, NA = missing (complete required for m >= 2).
...	engine arguments; see scmix.

Value

Engine output list; see scmix for main fields.

Examples

d <- scmix_sim_mw3(n = 150, seed = 2)
eng <- scmix_engine(d$Y, K = 4, m = 1, n_iter = 200, burn = 80,
                    consensus = TRUE, seed = 3)
scmix_ari(eng$z_consensus, d$z)   # linear conditionals, short run

# quadratic conditionals at a more realistic length
eng2 <- scmix_engine(d$Y, K = 4, m = 2, n_iter = 400, burn = 200,
                     consensus = TRUE, seed = 3)
eng2$Kstar_consensus
scmix_ari(eng2$z_consensus, d$z)

---

Multiple imputation with the sparse conditional mixture engine

Description

Runs the same engine as scmix in multiple-imputation mode (linear conditionals, m = 1) for a data matrix with missing values, returning completed data sets and Rubin-pooling utilities.

Usage

scmix_impute(
  Y,
  M = 10L,
  K = 10L,
  n_iter = 1500L,
  burn = 500L,
  a = 1/K,
  seed = NULL,
  verbose = 0L,
  ...
)

Arguments

Y	numeric matrix with NAs.
M	number of completed data sets to return.
K	integer, overfitted cap on the number of components (the number of occupied components is estimated; K only needs to exceed the plausible truth). Default 7.
n_iter, burn	total and burn-in Gibbs sweeps.
a	Dirichlet concentration of the mixture weights (default 1/K; must be small for superfluous components to empty out).
seed	optional integer seed (full run reproducibility).
verbose	print progress every verbose sweeps (0 = silent).
...	further engine arguments.

Value

List with completed (list of M completed matrices) and the fitted-model summaries of scmix.

See Also

rubin_pool_scmix

Examples

Y <- scmix_sim_mw3(n = 120, seed = 7)$Y
set.seed(7)
Y[sample(length(Y), 30)] <- NA
imp <- scmix_impute(Y, M = 2, K = 4, n_iter = 300, burn = 100, seed = 8)
length(imp$completed)
anyNA(imp$completed[[1]])

---

Simulate the p = 3 replication setting of Melnykov and Wang (2023)

Description

Draws one data set from the three-component, quadratic-conditional setting of Melnykov and Wang (2023), supplementary Table S-1 (p = 3), as replicated in the accompanying paper.

Usage

scmix_sim_mw3(n = 1000, seed = NULL)

Arguments

n	Sample size.
seed	Optional seed.

Value

A list with elements Y (an n x 3 matrix) and z (the true component labels).

References

Melnykov, V. and Wang, Y. (2023). Conditional mixture modeling and model-based clustering. Pattern Recognition, 133:108994. doi:10.1016/j.patcog.2022.108994

Examples

d <- scmix_sim_mw3(n = 300, seed = 1)
dim(d$Y)
table(d$z)

---